Uninterrupted amplification key stimulated emission of radiation from a substance having three energy states



2,909,654 UNINTERRUPTED AMPLIFICATION KEY STIMULATED EMISSION N. BLOEMBERGEN Oct. 20, 1959 OF RADIATION, FROM A SUBSTANCE HAVING THREE ENERGY STATES Filed Oct. 15, 1956 FIG. I

2 m F N 5/ 5 0 m m FIG. 3

LOAD

UASER I IN VENT OR By M BLOEMBERGEN INPUT OUTPUT ATIOR/VE Y Un td StHIES J UNlNTER RUPTED AMPLIFICATION KEY STIMU- LATED EMISSION F RADIATION FROM A SUB- STANCE HAVING THREE ENERGY STATES Thisinvention relates to microwave amplification by stimulated emission of radiation. Apparatus for achieving such amplification is now generally described as a maser, a term which is an acronym for microwave amplification by stimulated emission of radiation.

The process of such amplification depends on the existence in a medium of discrete energy levels.

Normally, the population distribution among the possible energy levels in a medium is governed by Boltzmanns equation and, accordingly, in the system higher energy levels are less populated than lower energy levels. When electromagnetic Wave energy of the frequency proper to the, energy difierence between two particular levels in accordance with Plancks equation where h is Plancks constant) is applied to the medium, there will be an exchange between the populations of these levels; acertain fraction of the population in the lower level will absorb radiation and be raised to the higher levelj an equal fraction of the population in the higher level will be stimulated to emit radiation and will drop to the lower level. When, as is normally the case, there is a greater population in the lower level, the result will be a net absorption of energy.

On the other hand, if there be provided a medium in which for a finite time an upper energy level is more densely populated than a lower level, there can' be n'et emission; an incident radio signal of afrequency proper to the diiference in energy of these levels will for such time cause more power of such frequency to be radiated than is absorbed, whereby amplification of the radio signal results. This is the basic principle of a maser.

Accordingly, in a maser there must be provided a medium in which the population of an upper energy level is greater than that of a lower energy value. Such a distribution, however, is not in thermal equilibrium. It will be convenient'to describe a medium which is in this condition as exhibiting a negative temperature. It is a characteristic of masers that ideally they have a noise figure considerably lower than the noise figure of other known forms of microwave amplifiers. Such lower noise figure can be utilized to provide a much higher sensitivity.

It is thought helpful to discuss briefly the prior art masers before proceeding to a description of the present invention.

In a paper entitled Amplification of Microwave Radiation by Substances Not in Thermal Equilibrium, by J. Weber, published in the Transactions of the I.R.E. Professional Group in Electron Devices, pages l-4, June 1953, it is shown to be possible to obtain coherent microwave radiation from crystals and gases, provided a nonequilibrium energy distribution is first produced. For achieving a system having the desired nonequilibrium energy distribution, it is suggested that a magnetic field be applied to an ensemble of molecules of a gas or nuclei 2,909,654 Patented Oct. 20, 1959 2 of a crystal lattice having a magnetic dipole moment. There will result an equilibrium distribution in the spins corresponding to upper energy parallel and lower energy anti-parallel states. Under these conditions a radio frequency signal of frequency corresponding to the difference between the lower and higher energy states in accordance with Plancks equation tends to be absorbed by the medium. Then if the direction of the applied magnetic field is reversed in a time short compared to the time it takes for the spins to follow, until equilibrium is restored, there will be more spins in the high energy state than in the low energy state and for such time amplification of the radio frequency signal is possible. However, hitherto it has proved difficult to construct a maser for operation in this way. The necessity for rapid reversal of'the direction of the applied magnetic field introduces serious practical difiiculties. Additionally, a maser of this type is by its nature poorly suited for amplification of a continuous radio frequency signal since it is inherently capable of useful amplification over only a limited portion of a complete cycle of operation.

Alternatively, in that paper it is further suggested that the desired nonequilibrium energy state may be provided by flowing ammonia gas through a region where an electric field is applied in which the Stark effect known to workers in the art is linear and which is characterized by an abrupt reversal in direction. In passing through the region of field reversal, the ammonia molecules should experience a change in rotational energy state which should result in a nonequilibrium distribution of rotational energy states.

In an article entitled, The MaserNew Type of Microwave Amplifier, Frequency Standard, and Spectrometer, Physical Review 99, 1264 (1955), there is described another previously known form of maser. In

this form, there is provided a molecular beam of ammonia which is made to traverse a region in which a. nonuniform electrostatic field is used to select for passage into a cavity substantially only those molecules which are in upper inversion energy states. There then results in the resonant cavity a gaseous medium in which the population of molecules in the upper inversion energy states exceeds that in the lower energy states. This corresponds to a medium which is at a negative temperature. Thereafter, by supplying further to the cavity a radio signal of frequency corresponding to the energy difference betwen the upper and lower inversion energy states, amplification of the radio signal is realized.

In discussing an oscillator which makes use of the maser principle the manner just described, it has further been suggested in a paper entitled Possible Methods of Obtaining Active Molecules for a Molecular Oscillator, published in the Journal of Experimental and Theoretical Physics, U.S.S.R, 26, pages 249-250 (February, 1955), that a molecular beam may be provided in which the population of molecules in an upper state exceeds the population of molecules in a lower state by preexposure of the molecular beam to auxiliary high frequency fields which induce resonance transitions between two levels which straddle an intermediate level. As a result, at saturation either the number of molecules in the highest of the three levels exceeds the number of molecules in the intermediate level or the number of molecules in the intermediate level exceeds the number in the lowest level. In either case, there is provided in the molecular beam the desired nonequilibriurn distribution of energy levels which can be used to provide radiation at the frequency corresponding to the diiference between the two appropriate energy levels.

Another known form of maser is described in a letter in Comptes Rendus 242, M51 (1956). In this form, a

silicon crystal doped with phosphorus is positioned in a cavity and thereafter subjected to a magnetic field which acts to line up parallel to it the spin magnetic moments of the conduction electrons. Thereafter, the magnitude of the applied magnetic field is varied to pass through the value corresponding to the electron spin resonance line in the manner similar to the adiabatic rapid passage technique used in nuclear magnetic resonance experiments known to workers in the art. This results in an inversion of the population of upper and lower spin levels, which provides the desired negative temperature in the medium for use in providing amplification to an incident radio frequency signal of the appropriate frequency. In this technique the negative temperature effect is discontinuous, existing only for the time it takes the spins to relax to equilibrium. After such time, another inversion is necessary if the negative temperature is to be reestablished. In order that the useful portion of an operating cycle belong, it is important to have a system in which the spin lattice relaxation time is long. This imposes severe limits on the materials which can be employed, particularly since increased relaxation time is achieved ordinarily only at the expense of a decrease in the number of the electrons in the crystal which participate in contributing to the negative temperature. Additionally, the amplification of a continuous wave is made quite complex by the inherently intermittent character of the negative temperature effect in the crystal.

' Still other techniques for achieving a negative temperature in a medium are described in United States Patent 2,762,871, which issued September 11, 1956. In one of the arrangements described, a paramagnetic solid is immersed in a magnetic field of strength chosen to give rise to resonance at a desired frequency in the material. Thereafter, a microwave pulse of the resonance frequency is applied to the material to invert the population distribution of the two energy states corresponding to the chosen resonance frequency in the manner known to workers in the art. As a consequence, the medium is put at a negative temperature and is made capable of amplifying an incident radio frequency signal of the resonance frequency for the relaxation time of the inverted system. Additionally, to avoid the difiiculties arising in this arrangement because the frequency of the energy applied to effect the inversion in population states must be identical with that at which the medium will thereafter amplify, there is proposed an alternative arrangement in which the medium is a gas confined to a closed chamber within which there is also included a Stark electrode. In this arrangement by means of the Stark effect, it is made possible to provide a difference in frequency between the microwave energy applied to effect the inversion in population states and the signal to be amplified. In an arrangement of this type utilizing the Stark effect in a confined gas, continuous operation is made possible, energy of one frequency being applied continuously to maintain the gas at a negative temperature, and incident signal energy of a different frequency being applied continuously to stimulate emission of radiation for its amplification.

From the foregoing description of the prior art, it appears that the only masers proposed hitherto which are inherently capable of continuous operation involve the use of a flowing or confined gas as the negative temperature medium. In addition to the obvious complexities in structure such use of a gas entails, it may be demonstrated that it is possible to achieve a considerably lower noise figure in a maser employing a solid as the negative temperature medium than in one employing a gas for this purpose, primarily because of the lower real temperature at which the solid may be operated.

Accordingly, the primary object of the present invention is to provide a solid state maser which is inherently capable of continuous operation. Additionally, it is advantageous that the maser have a relatively wide frequency band of operation, be readily tuned to the desired band of operation, be capable of handling relatively high powers, and have an inherently low noise level.

All these ends are achieved in a maser in accordance with the present invention.

A feature of the present invention is a solid state medium in which a negative temperature exists continuously during'operation. Such a medium comprises a paramagnetic solid which is characterized by a multiple energy level system with the separations of the energy levels fall ing within desired operating frequency ranges. To this solid, there is supplied continuously energy which effects transitions from a low energy level to a nonadjacent high energy level, bypassing an intermediate energy level. By power saturation of the high energy level, there can be established in the solid a nonequilibrium energy distribution with respect to the intermediate level, which can be used for the amplification of a signal of appropriate frequency. In particular, it is important to keep the solid at low temperatures to achieve fully the low noise advantage characteristic of a maser.

The invention will be better understood from the following more detailed description taken in conjunction with the accompanying drawings in which:

Fig. l is an energy diagram which will be helpful in explaining the principles of the invention;

Fig. 2 shows partly in schematic form and partly as a cross sectional view apparatus utilizing a solid as a negative temperature medium in accordance with the invention; and

Fig. 3 illustrates in schematic form a typical arrangement embodying a maser in accordance with the invention.

Before discussing in detail a specific embodiment of the invention, it Will be helpful to discuss the general principles applicable to the choice of solid for use as the medium which is to exhibit the desired negative tem-' perature in the practice of the invention.

Let us first for simplicity consider a solid having, at the low temperatures at which it is particularly advantageous to operate, a triplet ground state with the separation of the energy levels E E and E falling in the microwave range, as is shown in Fig. 1. Assume also that the probability of the transitions between energy levels E and E and between energy levels E and E is reasonably high. The various states will interact with the crystal lattice which is treated as a heat sink at the desired operating temperature. For the solid chosen this interaction is large compared with spontaneous and black body induced emission. It is characteristic of a maser in accordance with the invention that its feasibility is little affected by details of the relaxation mechanism of the energy levels of the solid used to provide the negative temperature medium. This is an additional advantage provided by the invention.

Suppose now that the system is initially in equilibrium with the lattice and that a local oscillator supplies microwave energy of the frequency corresponding to the sep aration of energy levels E and E to induce transitions from the former level to the latter level. The relative population of these two levels will come into a new equilibrium under the influence of the radiation and the spinlattice relaxation mechanism. If the intensity of thev applied local oscillator energy is sufficiently high and the relaxation time of the spin lattice sufficiently long, power saturation will occur between the two levels and the populations of levels E and E will be approximately equalized. In general, in this saturated condition, the population of intermediate level E Will either be greater or smaller than the equalized populations of levels E and E In the former case, maser action is possible at the frequency corresponding to the difference in energy levels E and E While in the latter case maser action is possible at the frequency corresponding to the difference in energy levels E and E Although, as shown, en-

ergy level E is .closer to energy level E in practice this is immaterial, the energy level i jrnay fall anywhere intermediate between the nonadj'acent energy levels E I It should be evident that, itflis'possible tojemploy the techniques .described'in an analogous manner'to achieve a negative temperature. in asolid having more than three energylevels, by making use'of transitionsof the kind described between any chosen three of such levels.

Various materials are possible for "use which satisfy the requirements outlined above. Of primary interest its preferred materials are ionically'bound paramagnetic salts." The choice of a particular paramagnetic salt is largely dependent on the existence of suitable energy levels and the existence of matrix elements of the magnetic moment operator between the various spin levels. The absorption and stimulated emission process depend directly on this operator, butthe relaxation times also dependon the spin angular 'mom'entumoperator via spin-orbitcoupling terms. It is importantthat-all offdiagonal elements between the three spin levelsunder consideration be nonvanishin'g. This is achieved by putting the paramagnetic salt with'a'crystalline fieldsplitting parameter 5 in a magnetic field which makes an angle with the crystalline field axis. The magnitude of this field is chosen such that the Zeeman energy is comparable to the crystalline field splitting. In this case, the. stateswith magnetic quantum numbers'm are all scrambled. 'Ihe mixing of the spin states by Zeemanand crystalline field interactions of comparable magnitude is important. The

energy levels and matrix elements ofthe spin angular momentum operator may be obtained by 'a numerical solution of the determinantal equation'of the spin Hamiltoniam When thelnumber ofelect'ron spin levels is greater than three, one may choosetherefrom three levels at which operation will take place.

" Paramagnetic salts which have previously been reported in. detail in the literature and which exhibit the properties desired include nickel fluosilicate' and gadolinium ethyl sulphate. Variousother ionically bound paramagnetic salts of the transition groups, such as iron and rare earth groups, exhibit similar properties.

The specific crystals mentioned have the advantage that all magnetic ions have the same crystalline field and nuclear hyperfine splitting is absent, which keeps the total number of possible transitions down.

The use of magnetically dilute salts is desirable to reduce the line width and to separate the individual resonance transitions. j

For example, a single crystal which is 95 percent ZnSiE -6H O and 5 percent the isomorphous nickel salt has a line width of 50 oersteds and an average crystalline field splitting 6 equal to .12 cm.- -for the nickel ions. 1 With an effective spinvalueequal to 1 there are three energy levels of importance and the. spin lattice relaxation time has been measured to, be about 10* seconds at .2" K. Relevantproperties of this salt are described in a paper published inthe Proceedings of the Physical Society A63,29 (1949").

Alternatively, a -single crystal which is. 99 percent I;a(( 3 H SO -9l-I O and one percent the isomonphous gadolinium salt has. an effective spin value S-=7/2. .In hero field there are four doublets separated respectively by a' crystalline field splitting 6 of .113 cmr j, .083 cmr and .046 cm. measured at 20 K. These splittings are substantially independent of temperature. The line width is seven oerstedsi This width may be reduced by a factor of three by using the deuterated salts. The relaxation time at 2 K. is about 10- seconds. Relevant properties of this salt are described. in a paper in the l?roceedings of the Royal Society A223, 15 (1954).

I .Itiis now convenient to describe by way of example for purposes of illustration the specific embodiment of the invention shown in Fig. 2, which uses as the negative temperature medium the diluted ,iiickel fluosi-licate crystal asoasso.

of the kind described above and which is designed particu: larly for amplification of a 1420 megacycle signal. The combination 10 includes a coaxial cavity 11 which is of a kind known to workers in the microwave art and has a fundamental mode resonating at the signal frequency and a higher mode resonating at the frequency of the driving microwave energy to be used to efiect the transitions from the low level E to the high level E In this embodiment, this frequency corresponds to 10,000 megacycles. Sinceit is desirable to be able to tune the cavity to the two resonance conditions independently, the coaxial cavity is provided with a dielectric element 12, advantageously a piece of rutile whose configuration resembles a sector of a circle 'and whose position is adjusted to tune the cavity at the higher of the two frequencies of interest. Because the element is positioned near a node in the electric field of the lower of the two frequencies of interest, its presence will little affect the tuning of the cavity at the lower fre quency. Additionally, for tuning the cavity to the lower frequency, there is provided a tuning screw 13 of the kind known to workers in the art.

7 There is included within the cavity a single crystal 14 ofthe diluted nickel fluosilicate salt. For a cavity having at the operating tmeperature of 2 K. a Q of 10 and an effective volume of 60 cm. it is calculated that the condition for amplification is satisfied if the total number of electron spins in the crystal exceeds 3x10 The required minimum number of nickel ions is contained in approximately .02 cm. of the nickel fluosilicate salt diluted as described. ,However, as may be expected, itwill generally be advisable to employ crystals largerthan the minimum size required.

There is also included apparatus 15 which provides a static magnetic field having a prescribed orientation with respect to the'crystalline axis as previously described. As will be known to workers in the art, the separations between the discrete energy levels, and hence the useful operating frequency ranges, will be controlled by the. strength of the static magnetic field applied. In the instant embodiment a field of approximately a thousand gauss is applied initially. However, it is convenient to adjust experimentally the magnitude and direction of the applied magnetic field to achieve the energy separations desired. Similarly, the orientation of the crystalline axis of the paramagnetic salt with respect to the radio frequency magnetic field is adjusted experimentally to give optimum values for the relevant matrix elements.

Microwave energy of the desired driving frequency is supplied by an excitation oscillator 16 and introduced into the cavity by a coupling probe 17 in the manner familiar to workers in the art. Enough poweris supplied to obtain saturation between energy levels E and Typically, saturation is obtained when the magnetic field of the driving energy has an intensity in the crystal of approximately 0.2 oersted.

It is generally characteristic that with paramagnetic salts the width of the band in which m-aser action is feasible is controlled by the strength of the driving magnetic field, because the line width is due to inhomogeneities in the internal fields of the paramagnetic salt. In the instant case, a field strength as described results in a useful band of about one-half a megacycle. Stronger fields result in a proportionate increase in the width of the useful band up to a maximum determined by the power handling ca 'pacity ofthe system.

Additionally, the input signal supplied from a suitable source, typically an antenna, is introduced into the-cavity by means of an input signal coupling probe 18.

The amplified signal is abstracted for utilization by a suitable load by way of an output coupling probe 19. In some instances, it is advantageous to employ the same coupling probe both to introduce and to abstract the signal energy as will be described in more detail hereinafter.

As has been indicated above, advantageously the cavity resonator is maintained at a temperature of about 2 K.

Various techniques will be known to a worker in the art to achieve this end. The broken line 20 is used to .indicate that the cavity and its contents are confined within Suitable refrigerating apparatus.

Itis of course feasible to operate at higher tempera tures. However, the higher the operating temperature the higher the noise level and the lower the spin lattice relaxation time. This latter eifect in turn results in a need for an increase in the driving magnetic field necessary to achieve saturation between the levels E and E Additionally, an increase in operating temperature results in an increase in the critical size of the crystal needed to obtain amplification.

It will, of course, be apparent that various other forms of cavity resonators may be utilized in analogous fashion in the practice of the invention. Similarly, other forms of coupling connections, such as loops, may be employed for supplying and abstracting the signal energyto the cavity as well as supplying the driving energy. Additionally, various other modifications such as the inclusion of mode suppressors are feasible. 7

Moreover, while the efficiency of a maser is enhanced by the use of a resonant cavity, it is feasible to employ instead a straight-through wave path, such as a hollow wave guide, a portion of which houses the medium exhibiting negative temperature. Typically, in such an arrangement, signal energy in traveling along the wave path is made to pass through the portion housing the medium which is at a negative temperature. Directional couplers advantageously may be used to couple the driving energy into the wave path from an auxiliary path. Various other arrangements of directional couplers and wave guides will be apparent to workers in the art for applying to the negative temperature medium both signal power and driving power.

A maser in accordance with the invention is capable of a variety of applications, as is characteristic generally of amplifiers. For example, if operated at a high enough gain, it can be made to oscillate, the noise inherent in the walls enclosing the medium acting initially tostimulate emission. The arrangement shown in Fig. 2 accordingly may be made to serve as an oscillator. In such a case, the input connection becomes superfluous and is advantageously omitted.

However, the maser has primary importance as a highly sensitive amplifier because of its low inherent noise level. It is characteristic that a maser has a linear gain response over a wide range of input levels. If the level of the input signal is suificient to cause saturation of the relevant transitions, the gain will automatically decrease. This reduces the need for any bum-out protection for the maser. A maser can readily be introduced to provide amplification at any point of an extended wave transmission system. Typically, however, a maser will find application as an amplifier in an arrangement of the kind shown in Fig. 3.

In this arrangement an antenna 21 is used to pick up transmitted signals and these signals are then supplied to arm a of a circulator 22. A circulator, as the term is understood in the microwave art, is a one way transmis sion element. In a paper entitled The Microwave Gyrator, published in the Bell System Technical Journal, volume 31, pages 1-31 (1952), there is described a circulator suitable for use in the arrangement being described. It is characteristic of such a circulator that energy supplied to arm a propagates therethrough selectively in the direction toward arm 11. Arm b of the circulator is used to supply input signal energy to the maser 23, which advantageously is of the kind shown in Fig. 2 with the exception that there is not included the coupling connection whichhas been described as the output coupling connection in the accompanying description. In this case instead, the output signal power is abstracted from the cavity by the same coupling loop which serves to introduce the signal power into the cavity. However, the out put power supplied to arm b from the cavity is-transmitted selectively through the circulator only in the direction .toward afm c. The maser is supplied with driving power from the local oscillator 24. Arm c of the-circulator in turn supplies 10511.25 which typically may be-a'receiver or the cavity of a second maser stage in instances wheremoregain is desired than it is convenient to realize in'a single maser stage. Any power reflected back by the load asa result of mismatches is transmitted through the circulator selectively only in the direction towards arm d. Arm d in turn-supplies a dummy load 26 which typically is .a matched termination designed to minimize reflections therefrom. 1 I

As previously indicated, to achieve maximum benefits of the improved noise characteristics of a maser in accordan ce with the inventiomit is advantageous to maintain it at a relatively low temperature, typically a few degrees Kelvin. However, to warrant operating the maser at such a temperature, it is also important to minimize noise from all other possible sources. Ordinarily, the antenna sees essentially the radiation temperature of inter; stellar space and so should not be a serious source of noise.

However, it would appear to be important to maintain the circulator, since it is a source of signal loss between the antenna and the maser, also at the low temperature at which the maser is operated. In the present instance where the circulator is operated at very low temperatures, it is possible to employ paramagnetic material rather than the usual ferromagnetic material in the gyrator which is a characteristic element of a circulator of the kind described in the aforementioned Bell System Technical Journal article. Such useof a paramagnetic material is feasible because at the low temperature involved the magnetization obtainable therein becomes largeenough. in Moreover, it would also appear advantageous to keep the dummy load at a low temperature. Because the circulator serves to isolate the useful load from the maser, no special precautions would appear to be necessary with respect to the useful load. I

In the drawing, the broken line 28 is used to denote that the elements enclosed thereby are kept within suitable refrigerating apparatus.

In the interest of simplicity, there has been avoided the showing of the various filter elements whose use would be obvious to a worker skilled in the art to minimize the transfer of the driving power to the useful load.

It should be understood that the specific arrangements described are merely illustrative of the general principles involved. Various modifications may be devised by a worker in the art without departing from the spirit and scope of the invention. In particular various materials having the desired distribution of energy levels are feasible. In particular, a maser in accordance with the invention may be made which uses changes in the nuclear quantum number. For example, there may be employed as the negative temperature medium a paramagnetic salt or an organic free radical with hyperfine structure, such that a hyperfine splitting is superimposed upon the electronic Zeeman splitting whereby multiple levels are provided. Transitions may then be induced between levels separated by one or more intermediate levels for achieving a nonequilibrium distribution in the medium which may be used for the emission of radiation.

Additionally, it should be evident that a maser of the kind described may find application in a variety of modulation arrangements. As has been described, in a maser in accordance with the invention, various parameters exist whose variation may be used to vary either the amplitude level of the output or the frequency response.

While the term maser suggests operation in the micro- 'wave range, it should be evident that by the choice of appropriate operating conditions amplification is possible even at frequenciesbelow what is usually regarded as the lower limit'of the microwave range. Acccordingly, for

9V the purposes ofthis'applicatiomthemicrowave range is defined a's' extending down to a lower limit'of at'least 100 megacycles. I M r o r, r c p es f. e invention-may .be extended toamultiple transition arrangements for providing maser action at a frequency higher than that of the driving power.,-1'To this end, there is chosen a solid, typically the gadolinium salt. previously described, which has at least four levels of increasingly higher energies, E E ,E and E ,'respe ctively; Driving power of appropriate frequency is supplied to the solid to induce transitions between levels E and E whereby saturation is achieved and the populations of the two levels are substantially equalized. Additionally, driving power of appropriate frequency is supplied. to'u the solid to induce transitions between the nonadjacent. levels E and 13,, whereby saturation is achieved landj thepopulations. of these two levels also are substantially equalized.

Under these conditions,'it is possible to achieve. a tion in the intermediatelevel E which is .larger' thanjthat in level E' To this end, ope rationat low cal. temperatures is especially important. Accordingly; signal 'power of frequency corresponding to 'the' separation in energy levels E and E may thereafterbe amplified. By appropriate choice of the operating parameters, it is possible to have the separation in levels E and E wider than that between levels E and E whereby amplification is possible at a frequency which is higher than either of those used for driving. Moreover, it should be evident that if the separation between energy levels E and E is made equal to the separation between nonadjacent energy levels E and E energy of a single driving frequency may be used to induce both transitions.

It is evident that other arrangements which involve multiple transitions are feasible.

What is claimed is:

1. In combination, a solid which is characterized by a multiple energy level system, means supplying driving energy to said solid for inducing enough transitions from one energy level to a non-adjacent, higher energy level of the system whereby the solid exhibits a negative temperature at a particular frequency, and means supplying to and abstracting from said solid energy of the particular frequency diiferent from the frequency of said driving energy and corresponding to the separation between a different pair of energy levels.

2. The combination of claim 1 in which the solid is an ionically bound paramagnetic salt. 7

3. The combination of claim 1 in which the solid is an ionically bound paramagnetic salt taken from the group consisting of the iron and rare earth transition groups. v

4. In combination, an ionically bound paramagnetic solid which is characterized by a multiple energy level system including at least three energy levels out of which a lowest, an intermediate and a highest are chosen, means supplying driving energy to said solid for inducing enough transistions from said lowest energy level to said highest energy level whereby the solid exhibits a nonequilibrium thermal distribution of energy states between said intermediate energy level and one of said lowest and highest energy levels, and means supplying to and abstracting from said solid energy of a frequency corresponding to the energy difference between said intermediate level and one of said other two levels whereby amplification results.

5. In combination, a cavity having at least two resonant modes, a solid which is characterized by a multiple energy level system positioned within said cavity, means supplying to the cavity driving energy at a frequency corresponding to one of the resonant modes of said cavity for inducing transitions between non-adjacent levels in said solid and establishing a negative temperature in modes of the cavity, .and means supplying to the solid energy at the last mentioned frequency for utilizingthe negative temperature of the solid for amplification,

. 6. The combination accordingto claim 5 in which the solid is an ionically boundparamagnetic salt. 7'. In an oscillator, a'cavity having at least two resonant modes, an ionically bound paramagnetic salt positioned within the cavity and characterized by a multiple energy level system having at least three'energy levels, the difference in energy between the lowest and highest of said three energy levels corresponding to one of the resonant frequencies of the cavity and the ditferen'ce in energy between the intermediate level of said three and one of said highest and lowest levels corresponding to another resonant frequency of said cavity, means supplying to said cavity driving energy of said one frequency for establishing a negativei'temperature in the salt at said other resonant frequency ofjthe cavity, and {means for abstracting oscillatory energy of said othei frequency from thecavity. v

8. In combination, a cavity having at least two resonant modes, an ionically bound paramagnetic salt which ispositioned in the cavity and which is characterized by a multiple energy level system including at least energy levels, means for supplying to the cavity driving microwave energy of a frequency corresponding to one of the resonant modes of the cavity for inducing transitions from said lowest level of said three to said highest level of said three for establishing a non-equilibrium thermal distribution of energy states in the salt with re spect to a different pair of the multiple energy levels whose separation corresponds to another resonant mode of the cavity, and means in energy exchange relation with the cavity for signal microwave energy of the frequency corresponding to the last-mentioned of the resonant modes of the cavity for amplification.

9. A combination according to claim 8 in which the solid is a nickel fluosilicate salt.

10. A combination according to claim 8 in which the sdlid is a gadolinium salt.

11. In combination, a cavity which has at least two resonant modes of different frequencies, an ionically bound paramagnetic crystal positioned in said cavity and characterized by a multiple energy level system including at least three levels, means for impressing a static magnetic field on said crystal of strength that the difference in energy levels between the lowest and highest levels of said three corresponds to a higher of the resonant frequencies of the cavity and the difference in energy level between the intermediate level of said three and one of said highest and lowest levels corresponds to -a lower of the resonant frequenciesof the cavity, means for supplying to the cavity driving energy of said higher frequency for establishing a negative temperature in V the cavity for energy of said lower frequency.

12. The combination of claim 11 in which said means in energy exchange relation comprises means for supplying signal energy for amplification and for abstracting amplified signal energy for utilization.

13. The combination of claim 11 in which said means in energy exchange relation comprises means for abstractng oscillatory energy.

14. Receiving apparatus comprising amplifying apparatus including a solid which is characterized by a multiple energy level system and to which is supplied driving energy of a frequency corresponding to the difference in energy levels between two non-adjacent levels whereby the solid is made to exhibit a negative temperature with respect to a difierent pair of energy levels of the multiple energy system, a source of signals, a load, and a circulator having a plurality of arms of which one is supplied by a source of signals with signal energy of a frequency suitable for amplification by the amplifying apparatus, an-

the solid at the frequency of another of the resonant other of which supplies signal energy to the amplifying Iap ia a'ms'and abstracts amplified signal povver merira of adjacent energy levels and one pair of nonadjacent energy levels of said four energy level systefn whereby a negative temperature with respect to another 'pair of nonadjacent energy levels of said. four energy level system is achieved, and m'eans'supplying to and abstracting from the solid signal povver of "frequency corresponding to the negative temperature in the solid. v

18. Receiving apparatus in accordance with claim 14 further characterized in that the source of signals is an antenna. a

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Article: Elec tronic Structure of F Centers by Ki'p'et 211., Physical Review, vol. 91, No. 5, pages 1066- 1071, se t 1953; I I a 7 Article: Possible fMethodsof Obtaining Active Mole- 'c'u'les for a Molecular'Oscillator by Basov. et al., U.S S .R., l Exper. 'Theor. Phys. 'U.S.S.R. 28, 249450 for February '1'955,'as translated and 'publishedfin Soviet PhysicsjlEzf-Il'P voL .1, No. l, July-1955, pages 184 -185. Article: "Electronic"Structure of F Centers ,by Porti's, Physical Review, vol. 91, No. 5, pages 1071-1078, Sept; 1, 1953. I l 

